On the classifying space for proper actions

2001 ◽  
pp. 263-269 ◽  
Author(s):  
Guido Mislin
Keyword(s):  
Classifying Space ◽  
Proper Actions

scholarly journals On the classifying space for proper actions of groups with cyclic torsion

2014 ◽  
Vol 26 (1) ◽  
Author(s):  
Yago Antolín ◽  
Ramón Flores
Keyword(s):  
Classifying Space ◽  
Proper Actions ◽  
Cyclic Torsion

scholarly journals INJECTIVE HULLS OF CERTAIN DISCRETE METRIC SPACES AND GROUPS

2013 ◽  
Vol 05 (03) ◽  
pp. 297-331 ◽  
Author(s):  
URS LANG
Keyword(s):  
Metric Spaces ◽  
Positive Curvature ◽  
Hyperbolic Group ◽  
Finite Graph ◽  
Barycentric Subdivision ◽  
Classifying Space ◽  
Polyhedral Complex ◽  
Locally Finite ◽  
Proper Actions ◽  
Locally Finite Graph

Injective metric spaces, or absolute 1-Lipschitz retracts, share a number of properties with CAT(0) spaces. In the '60s Isbell showed that every metric space X has an injective hull E (X). Here it is proved that if X is the vertex set of a connected locally finite graph with a uniform stability property of intervals, then E (X) is a locally finite polyhedral complex with finitely many isometry types of n-cells, isometric to polytopes in [Formula: see text], for each n. This applies to a class of finitely generated groups Γ, including all word hyperbolic groups and abelian groups, among others. Then Γ acts properly on E(Γ) by cellular isometries, and the first barycentric subdivision of E(Γ) is a model for the classifying space [Formula: see text] for proper actions. If Γ is hyperbolic, E(Γ) is finite dimensional and the action is cocompact. In particular, every hyperbolic group acts properly and cocompactly on a space of non-positive curvature in a weak (but non-coarse) sense.

scholarly journals Hecke operators in Bredon (co)homology, K-(co)homology and Bianchi groups

2021 ◽  
pp. 1-32
Author(s):  
David Muñoz ◽  
Jorge Plazas ◽  
Mario Velásquez
Keyword(s):  
Spectral Sequence ◽  
Discrete Group ◽  
Hecke Operators ◽  
Classifying Space ◽  
Main Interest ◽  
Proper Actions

In this paper, we provide a framework for the study of Hecke operators acting on the Bredon (co)homology of an arithmetic discrete group. Our main interest lies in the study of Hecke operators for Bianchi groups. Using the Baum–Connes conjecture, we can transfer computations in Bredon homology to obtain a Hecke action on the [Formula: see text]-theory of the reduced [Formula: see text]-algebra of the group. We show the power of this method giving explicit computations for the group [Formula: see text]. In order to carry out these computations we use an Atiyah–Segal type spectral sequence together with the Bredon homology of the classifying space for proper actions.

Spaces of PL Manifolds and Categories of Simple Maps (AM-186)

2013 ◽  
Author(s):  
Friedhelm Waldhausen ◽  
Bjørn Jahren ◽  
John Rognes
Keyword(s):  
Main Tool ◽  
Homotopy Equivalence ◽  
Classifying Space ◽  
Deformation Retract ◽  
Simplicial Sets ◽  
Full Proof

Since its introduction by the author in the 1970s, the algebraic K-theory of spaces has been recognized as the main tool for studying parametrized phenomena in the theory of manifolds. However, a full proof of the equivalence relating the two areas has not appeared until now. This book presents such a proof, essentially completing the author's program from more than thirty years ago. The main result is a stable parametrized h-cobordism theorem, derived from a homotopy equivalence between a space of PL h-cobordisms on a space X and the classifying space of a category of simple maps of spaces having X as deformation retract. The smooth and topological results then follow by smoothing and triangulation theory. The proof has two main parts. The essence of the first part is a “desingularization,” improving arbitrary finite simplicial sets to polyhedra. The second part compares polyhedra with PL manifolds by a thickening procedure. Many of the techniques and results developed should be useful in other connections.

scholarly journals Achieving a Sustainable Development Process by Deployment of Solar PV Power in ASEAN: A SWOT Analysis

Processes ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 630
Author(s):  
Hengtian Wang ◽  
Xiaolong Yang ◽  
Qihe Lou ◽  
Xinxin Xu
Keyword(s):  
Sustainable Development ◽  
Development Process ◽  
Swot Analysis ◽  
Primary Energy ◽  
Solar Pv ◽  
Proper Actions ◽  
External Threats ◽  
Process Deployment ◽  
Asean Countries ◽  
Primary Energy Supply

The Association of Southeast Asian Nations (ASEAN) has experienced rapid social and economic development in the past decades, while energy shortage, environmental pollution, and climate change are the factors that prevent a sustainable development process. Deployment of solar photovoltaic (PV) power is one of the effective alternatives to overcome the above barriers and assist ASEAN to achieve the aspirational target of 23% renewable energy (RE) in the total primary energy supply (TPES). In this study, SWOT analysis is adopted to analyze the internal strengths and weaknesses and the external threats and opportunities tightly related to the development of solar PV power in ASEAN countries. Through the SWOT analysis, great potential for the development of solar PV power in ASEAN is found. As long as appropriate policies are implemented and proper actions are taken, huge space for deployment of solar PV power can be expected. Based on the SWOT analysis, countermeasures that emphasize further deployment of solar PV power in ASEAN countries are put forward. The tactics include arousing people’s awareness of a sustainable development process, government issue coherence and stable incentive policies, fostering a solar PV industry chain and master key technology, and seek opportunities via an international cooperation.

Stable decompositions of classifying spaces of finite abelianp-groups

1988 ◽  
Vol 103 (3) ◽  
pp. 427-449 ◽  
Author(s):  
John C. Harris ◽  
Nicholas J. Kuhn
Keyword(s):  
Finite Group ◽  
Cohomology Theory ◽  
Classifying Spaces ◽  
Classifying Space ◽  
Image Position ◽  
A Finite Group

LetBGbe the classifying space of a finite groupG. Consider the problem of finding astabledecompositionintoindecomposablewedge summands. Such a decomposition naturally splitsE*(BG), whereE* is any cohomology theory.

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